Míry rizika-dynamika, citlivost
Risk measures - sensitivity and dynamics
rigorous thesis (RECOGNIZED)
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Permanent link
http://hdl.handle.net/20.500.11956/15188Identifiers
Study Information System: 60043
Collections
- Kvalifikační práce [10678]
Author
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, mathematical statistics and econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
26. 5. 2008
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
Czech
Grade
Recognized
Risk measures are subject to many scientific papers and monographs published on financial portfolio optimization problem within stochastic programming. Currently there are many functionals which measure risk of random future losses according to risk managers preferences. However, their sensitivity is studied less commonly, especially according to possible changes of input data or with respect to the portfolio allocation. This thesis deals with sensitivity of two frequently discussed measures - Value at Risk (VaR) and Conditional Value at Risk (CVaR). Explicit contamination bounds for relative VaR optimization problem are expressed using general results of parametric optimization valid for quadratic programming. A numerical study and a heuristic algorithm for correlation matrices stressing are involved. Sensitivity of VaR and CVaR is studied through their derivatives with respect to the portfolio allocation. Assumptions for the derivatives are formulated, Hessians introduced and convexity is discussed. At last, some dynamic risk measures for multi-period investory models are proposed.